Question

let T:R^2 to R^2 be linear operator given by formula T(x,y)=(2x-y,-8x+4y) then which of the following vectors are in kernal(T)
a)(5,10)
b)(3,2)
c)(1,1)

Answer 1

a

Answer 2

its because T(5,10)=(0,0)
right?! :)

Answer 3

if a vector, say v, is in the kernal(T), then that means T(v) = 0, so lets plug in the vectors and see which one comes out to 0:
T(5,10) = (2(5)-10, -8(5)+4(10)) = (10-10, -40+40) = (0,0)
wow thats luck lol, its a.

Answer 4

on a side note, i dont like calling it the Kernal, i like calling it the Null Space. Sounds much more awesome lol

Answer 5

thank you sir i got the answer